{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "D = {'death_rate': np.array([6.2300e-03, 4.4000e-04, 2.7000e-04, 2.0000e-04, 1.6000e-04,\n",
    "       1.2000e-04, 1.1000e-04, 1.1000e-04, 1.2000e-04, 1.1000e-04,\n",
    "       1.0000e-04, 1.3000e-04, 1.3000e-04, 1.5000e-04, 2.0000e-04,\n",
    "       2.5000e-04, 3.7000e-04, 4.7000e-04, 6.4000e-04, 7.1000e-04,\n",
    "       7.6000e-04, 8.7000e-04, 8.7000e-04, 8.8000e-04, 9.4000e-04,\n",
    "       9.2000e-04, 9.5000e-04, 9.3000e-04, 9.9000e-04, 1.0100e-03,\n",
    "       1.0300e-03, 1.0900e-03, 1.1000e-03, 1.1400e-03, 1.1500e-03,\n",
    "       1.2000e-03, 1.3100e-03, 1.3700e-03, 1.4600e-03, 1.5600e-03,\n",
    "       1.6200e-03, 1.8500e-03, 2.0100e-03, 2.1600e-03, 2.4300e-03,\n",
    "       2.5800e-03, 2.9800e-03, 3.2500e-03, 3.5100e-03, 3.8700e-03,\n",
    "       4.1300e-03, 4.5400e-03, 4.9400e-03, 5.3300e-03, 5.7100e-03,\n",
    "       6.0200e-03, 6.7000e-03, 7.1000e-03, 7.6900e-03, 8.2800e-03,\n",
    "       8.6000e-03, 9.3200e-03, 9.9800e-03, 1.1010e-02, 1.2500e-02,\n",
    "       1.2820e-02, 1.4040e-02, 1.5150e-02, 1.6870e-02, 1.8300e-02,\n",
    "       1.9670e-02, 2.1330e-02, 2.3470e-02, 2.5620e-02, 2.8000e-02,\n",
    "       3.0830e-02, 3.4410e-02, 3.7110e-02, 4.1260e-02, 4.4480e-02,\n",
    "       4.9640e-02, 5.5390e-02, 6.1490e-02, 6.8030e-02, 7.6730e-02,\n",
    "       8.5610e-02, 9.5400e-02, 1.0636e-01, 1.1802e-01, 1.3385e-01,\n",
    "       1.5250e-01, 1.6491e-01, 1.8738e-01, 2.0757e-01, 2.2688e-01,\n",
    "       2.5196e-01, 2.7422e-01, 2.9239e-01, 3.2560e-01, 3.4157e-01]), 'population': np.array([3.94415, 3.97807, 4.09693, 4.11904, 4.06317, 4.05686, 4.06638,\n",
    "       4.03058, 4.04649, 4.14835, 4.17254, 4.11442, 4.10624, 4.11801,\n",
    "       4.16598, 4.24282, 4.31614, 4.39529, 4.50085, 4.58523, 4.51913,\n",
    "       4.35429, 4.26464, 4.19857, 4.24936, 4.26235, 4.15231, 4.24887,\n",
    "       4.21525, 4.22308, 4.28567, 3.97022, 3.98685, 3.88015, 3.83922,\n",
    "       3.95643, 3.80209, 3.93445, 4.12188, 4.3648 , 4.38327, 4.11498,\n",
    "       4.0761 , 4.10511, 4.2115 , 4.50887, 4.51976, 4.53526, 4.5388 ,\n",
    "       4.6059 , 4.66029, 4.46463, 4.50085, 4.38035, 4.292  , 4.25471,\n",
    "       4.03751, 3.93639, 3.79493, 3.64127, 3.62113, 3.4926 , 3.56318,\n",
    "       3.48388, 2.65713, 2.68076, 2.63914, 2.64936, 2.32367, 2.14232,\n",
    "       2.04312, 1.94932, 1.86427, 1.73696, 1.68449, 1.62008, 1.47107,\n",
    "       1.45533, 1.40012, 1.37119, 1.30851, 1.21287, 1.16142, 1.07481,\n",
    "       0.98572, 0.91472, 0.81421, 0.71291, 0.64062, 0.538  , 0.43556,\n",
    "       0.34499, 0.28139, 0.21698, 0.16944, 0.12972, 0.09522, 0.06814,\n",
    "       0.0459 , 0.03227]), 'birth_rate': np.array([0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,\n",
    "       0.     , 0.     , 0.     , 0.0002 , 0.0002 , 0.0002 , 0.0002 ,\n",
    "       0.0002 , 0.0171 , 0.0171 , 0.0171 , 0.0171 , 0.0171 , 0.045  ,\n",
    "       0.045  , 0.045  , 0.045  , 0.045  , 0.05415, 0.05415, 0.05415,\n",
    "       0.05415, 0.05415, 0.04825, 0.04825, 0.04825, 0.04825, 0.04825,\n",
    "       0.0225 , 0.0225 , 0.0225 , 0.0225 , 0.0225 , 0.0051 , 0.0051 ,\n",
    "       0.0051 , 0.0051 , 0.0051 , 0.00035, 0.00035, 0.00035, 0.00035,\n",
    "       0.00035, 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,\n",
    "       0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,\n",
    "       0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,\n",
    "       0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,\n",
    "       0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,\n",
    "       0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,\n",
    "       0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,\n",
    "       0.     , 0.     ])}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/vb/anaconda3/lib/python3.7/site-packages/matplotlib/__init__.py:846: MatplotlibDeprecationWarning: \n",
      "The text.latex.unicode rcparam was deprecated in Matplotlib 2.2 and will be removed in 3.1.\n",
      "  \"2.2\", name=key, obj_type=\"rcparam\", addendum=addendum)\n",
      "/Users/vb/anaconda3/lib/python3.7/site-packages/matplotlib/__init__.py:855: MatplotlibDeprecationWarning: \n",
      "examples.directory is deprecated; in the future, examples will be found relative to the 'datapath' directory.\n",
      "  \"found relative to the 'datapath' directory.\".format(key))\n",
      "/Users/vb/anaconda3/lib/python3.7/site-packages/matplotlib/__init__.py:947: UserWarning: could not find rc file; returning defaults\n",
      "  warnings.warn(message)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import numpy.linalg as npl\n",
    "import math\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 9.1 Linear Dynamical Systems"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((3, 50),\n",
       " array([[ 1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "          0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "          0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "          0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "        [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "          0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "          0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "          0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "        [-1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "          0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "          0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "          0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]]))"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.matrix([[.97,.1,-.05],[-.3,.99,.05],[.01,-.04,.96]]) \n",
    "#dynamics matrix where each row represents coefficients affecting one variable\n",
    "initX = np.array([1,0,-1]) #the variables for each row^\n",
    "time = 50\n",
    "storeinstances = np.zeros((len(initX),time-1))\n",
    "stateTraj = np.vstack((initX,storeinstances.transpose())).transpose()\n",
    "np.shape(stateTraj), stateTraj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.02, -0.35, -0.95])"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for t in range(time-1):\n",
    "    #J: stateTraj[:,t+1] = A*state_traj[:,t]\n",
    "    stateTraj[:,t+1] = np.matmul(A,stateTraj[:,t])\n",
    "    #[:,t] is grabbing each column as an array, which numpy handles the same as Julia\n",
    "    #matmul is getting the sum of multiplying each item in the array grabbed by [:,t] with their respective row in A\n",
    "stateTraj[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11c296a58>"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "[plt.plot(range(time),stateTraj[i]) for i in range(len(stateTraj))]\n",
    "plt.legend([\"x1\",\"x2\",\"x3\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 9.2 Population Dynamics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('pop:',\n",
       " array([4.51913, 4.35429, 4.26464, 4.19857, 4.24936]),\n",
       " 'death:',\n",
       " array([0.00076, 0.00087, 0.00087, 0.00088, 0.00094]),\n",
       " 'birth:',\n",
       " array([0.045, 0.045, 0.045, 0.045, 0.045]))"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "population = D['population']\n",
    "deathRate = D['death_rate']\n",
    "birthRate = D['birth_rate']\n",
    "'pop:',population[20:25],'death:',deathRate[20:25],'birth:',birthRate[20:25]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 385,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(population)\n",
    "plt.grid(True)\n",
    "#population in millions at each age (US 2010)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 424,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11d022978>]"
      ]
     },
     "execution_count": 424,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(birthRate)\n",
    "#proportion of ages at which adults gave birth to a child (US 2010)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 388,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11c971128>]"
      ]
     },
     "execution_count": 388,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(deathRate)\n",
    "#proportion of ages at which adults died (US 2010)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 431,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make a dynamics matrix representing birth and death rates \n",
    "diagDeath = np.diag(1-deathRate[0:len(deathRate)-1])\n",
    "zerosDeath = np.vstack(np.zeros(len(diagDeath)))\n",
    "A = np.block([[birthRate],[diagDeath,zerosDeath]])\n",
    "\n",
    "    \n",
    "plt.plot(population)\n",
    "pop2 = D[\"population\"]\n",
    "#iterate however (k) many years you want to simulate\n",
    "for k in range(10):\n",
    "    pop2 = np.matmul(A,pop2)\n",
    "    plt.plot(pop2)\n",
    "\n",
    "#population age shifting to the right  \n",
    "#and population count shiting down slightly over k (10) years"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 9.3 Epidemic Dynamics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 471,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11d623400>"
      ]
     },
     "execution_count": 471,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "T  = 210 #number of days\n",
    "A = np.matrix([[.95,.04,0,0],[.05,.85,0,0],[0,.1,1,0],[0,.01,0,1]]) #dynamics matrix\n",
    "x1 = np.array([1,0,0,0]) #initial state: everyone healthy\n",
    "stateTraj = np.hstack([np.vstack(x1),np.zeros((4,T-1))]) #initialize trajectory with 0s\n",
    "for t in range(T-1):\n",
    "    stateTraj[:,t+1] = np.matmul(A,stateTraj[:,t])\n",
    "\n",
    "for i in range(len(stateTraj)):\n",
    "    plt.plot(range(T),stateTraj[i])\n",
    "\n",
    "plt.legend([\"Susceptible\",\"Infected\",\"Recovered\",\"Deceased\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 9.4 Motion of a Mass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 597,
   "metadata": {},
   "outputs": [],
   "source": [
    "h,m,eta = .01,1,1\n",
    "A = np.matrix([[1,h],[0, 1-h*eta/m]])\n",
    "B = np.matrix([[0],[h/m]])\n",
    "x1 = np.array([0,0])\n",
    "K = 300 #3 second simulation\n",
    "f = np.zeros(K)\n",
    "f[50:99] = 1.0\n",
    "f[100:139] = -1.3\n",
    "X = np.hstack([np.vstack(x1),np.zeros((2,K-1))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 598,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10d39ab00>"
      ]
     },
     "execution_count": 598,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for k in range(K-1):\n",
    "    X[:,k+1] = np.matmul(A,X[:,k]) + np.hstack(B*f[k])\n",
    "\n",
    "plt.plot(X[0])\n",
    "plt.plot(X[1])\n",
    "plt.legend([\"position\",\"velocity\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 9.5 Supply Chain Dynamics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Nothing in Julia companion but textbook has an incidence matrix \n",
    "#and dynamics matrix plotted on a graph that networkX might be able to do"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
